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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Peter Imkeller

Publications 1997 -

L. Arnold, P. Imkeller
Normal forms for stochastic differential equations. Probab. Theory Relat. Fields 110 (1998), No.4, 559-588
P. Imkeller
The smoothness of laws of random flags and Oseledets spaces of linear stochastic differential equations. Potential Anal. 9 (1998), No.4, 321-349
P. Imkeller, M. Scheutzow
On the spatial behaviour of stochastic flows in Euclidean space. Ann. Probab. 27 (1999), No.1, 109-129
L. Arnold, P. Imkeller
On the integrability condition in the multiplicative ergodic theorem for stochastic differential equations. Stochastics Stochastics Rep. 64 (1998), No. 3-4, 195-210
F. Weisz, P. Imkeller
Critical dimensions for the existence of self-intersection local times of the n-parameter Brownian motion in R^d. J. Theor. Probab. 12 (1999), No.3, 721-737
L. Arnold, P. Imkeller
Rotation numbers for linear stochastic differential equations.  Ann. Probab. 27(1999), No.1, 130-149
P. Imkeller, C. Lederer
An explicit description of the Lyapunov exponents of the noisy damped harmonic oscillator. Dyn. Stab. Syst. 14 (1999), No.4, 385-405
H. Crauel, P. Imkeller, M. Steinkamp
Bifurcation of one dimensional stochastic differential equations.  Crauel, Hans (ed.) et al., Stochastic dynamics. Conference on Random dynamical systems, Bremen, Germany, April 28 - May 2, 1997. Dedicated to Ludwig Arnold on the occasion of his 60th birthday. New York, NY: Springer (1999), 27-47
J. Amendinger, P. Imkeller, M. Schweizer
Additional logarithmic utility of an insider.  Stochastic Processes Appl. 75 (1998), No.2, 263-286
P. Imkeller, F. Weisz
Double points of the Brownian sheet in R^d and the geometry of the parameter space. Stochastics Stochastics Rep. 70 (2000), No.3-4, 165-211
L. Arnold, P. Imkeller,
The Kramers oscillator revisited. Lecture Notes in Physics, Springer Verlag Berlin, vol. 557 (2000), pp. 280-291
L. Arnold, P. Imkeller, N.S. Namachchivaya
The asymptotic stability of weakly perturbed two dimensional Hamiltonian systems. Proceedings of 18-th Biennial Conference on Mechanical Vibration and Noise ASME Design Engineering Technical Conferences September 9-12, 2001, Pittsburgh, Pennsylvania, USA
L. Arnold, P. Imkeller, N.S. Namachchivaya
The asymptotic stability of a noisy non-linear oscillator. Journal of Sound and Vibration, vol. 269 (2001), Issues 3-5, pp 1003-1029
P. Imkeller, B. Schmalfuss
The conjugacy of stochastic and random differential equations and the existence of global attractors. J. Dyn. Differ. Equations 13 (2001), No.2, 215-249
P. Imkeller, C. Lederer
On the cohomology of stochastic and random differential equations. Probab. Theory Relat. Fields 120 (2001), No.2, 209-235
P. Imkeller, C. Lederer
Some formulas for Lyapunov exponents and rotation numbers in two dimensions and the stability of the harmonic oscillator and the inverted pendulum. Dyn. Syst. 16 (2001), No. 1, 29-61
P. Imkeller, M. Pontier, F. Weisz
Free lunch and arbitrage possibilities in a financial market model with an insider. Stochastic Processes Appl. 92 (2001), No. 1, 103-130
P. Imkeller
Energy balance models - viewed from stochastic dynamics.  Imkeller, Peter (ed.) et al., Stochastic climate models. Proceedings of a workshop, Chorin, Germany, Summer 1999. Basel: Birkhäuser. Prog. Probab. 49 (2001), 213-240
A. Monahan, L. Pandolfo, P. Imkeller
Stochastic confinement of Rossby waves by fluctuating eastward flows.  Imkeller, Peter (ed.) et al., Stochastic climate models. Proceedings of a workshop, Chorin, Germany, Summer 1999. Basel: Birkhäuser. Prog. Probab. 49 (2001), 325-343
P. Imkeller, A. Monahan, L. Pandolfo
Some mathematical remarks concerning the localization of planetary waves in a stochastic background flow.  Imkeller, Peter (ed.) et al., Stochastic climate models. Proceedings of a workshop, Chorin, Germany, Summer 1999. Basel: Birkhäuser. Prog. Probab. 49 (2001), 345-368
P. Imkeller, I. Pavlyukevich
Stochastic resonance in two-state Markov chains.  Arch. Math. 77 (2001), No.1, 107-115
P. Imkeller
Random times at which insiders can have free lunches.  Stochastics Stochastics Rep. 74 (2002), No. 1-2, 465-487
P. Imkeller, G. Milstein
Moment Lyapunov exponent for conservative systems with small periodic and random perturbations. Stoch. Dyn. 2 (2002), No.1, 25-48
P. Imkeller, C. Lederer
The cohomology of stochastic and random differential equations, and local linearization of stochastic flows.  Stoch. Dyn. 2 (2002), No.2, 131-159
S. Herrmann, P. Imkeller
Barrier crossings characterize stochastic resonance.  Stoch. Dyn. 2 (2002), No.3, 413-436
P. Imkeller, I. Pavlyukevich
Model reduction and stochastic resonance.  Stoch. Dyn. 2 (2002), No.4, 463-506
P. Imkeller, A. Monahan
Conceptual stochastic climate models.  Stoch. Dyn. 2 (2002), No.3, 311-326
P. Imkeller, I. Pavlyukevich
The reduction of potential diffusions to finite state Markov chains and stochastic resonance.  Sri Namachchivaya, N. (ed.) et al., IUTAM symposium on nonlinear stochastic dynamics. Proceedings of the IUTAM symposium, Monticello, IL, USA, Augsut 26--30, 2002. Dordrecht: Kluwer Academic Publishers. Solid Mech. Appl. 110 (2003), 57-69
S. Herrmann, P. Imkeller, I. Pavlyukevich
Stochastic Resonance: non-robust and robust tuning notions. in: K. Haman, B. Jakubiak and J. Zabczyk (eds.), Probabilistic Problems in Atmospheric and Water Sciences. Proceedings of the Workshop held at the Bedlewo Mathematical Conference Center, December 16-18, 2002, Banach Center Publ., 2003
L. Arnold, P. Imkeller, Y. Wu
Reduction of deterministic coupled atmosphere-ocean models to stochastic ocean models: a numerical case study of the Lorenz-Maas system.  Dyn. Syst. 18 (2003), No. 4, 295-350
P. Imkeller, P.Kloeden
On the computation of invariant measures in random dynamical systems. Stoch. Dyn. 3 (2003), No. 2, 247-265
P. Imkeller
Malliavin's calculus in insider models: additional utility and free lunches.  Math. Finance 13 (2003), No. 1, 153-169
J. M. Corcuera, P. Imkeller, A. Kohatsu-Higa, D. Nualart
Additional utility of insiders with imperfect dynamical information.  Finance Stoch. 8 (2004), No. 3, 437-450
P. Imkeller, I. Pavlyukevich
Stochastic resonance: a comparative study of two-state models.  Dalang, Robert C. (ed.) et al., Seminar on stochastic analysis, random fields and applications IV, Centro Stefano Franscini, Ascona, Switzerland, May 20--24, 2002. Proceedings. Basel: Birkhäuser. Progress in Probability 58 (2004), 141-154
S. Herrmann, P. Imkeller
The exit problem for diffusions with time periodic drift and stochastic resonance.  Ann. Appl. Probab. 15 (2005), No. 1A, 39-68
S. Ankirchner, P. Imkeller
Finite utility on financial markets with asymmetric information and structure properties of the price dynamics.  Ann. Inst. Henri Poincaré, Probab. Stat. 41 (2005), No. 3, 479-503
Y. Hu, P. Imkeller, M. Müller
Partial equilibrium and market completion.  Int. J. Theor. Appl. Finance 8 (2005), No. 4, 483-508
S. Herrmann, P. Imkeller, I. Pavlyukevich
Two mathematical approaches to stochastic resonance.  Deuschel, Jean-Dominique (ed.) et al., Interacting stochastic systems. Berlin: Springer (2005), 327-351
Y. Hu, P. Imkeller, M. Müller
Utility maximization in incomplete markets.  Ann. Appl. Probab. 15 (2005), No. 3, 1691-1712
M. Fischer, P. Imkeller
A two state model for noise-induced resonance in bistable systems with delays. Stoch. Dyn. 5 (2005), No. 2, 247-270
S. Chaumont, U. Horst P. Imkeller, M. Müller
A simple model for trading climate risk. Vierteljahrshefte zur Wirtschaftsforschung 74 (2005), 2, 175-195
S. Chaumont, P. Imkeller, M. Müller
Equilibrium trading of climate and weather risk and numerical simulation in a Markovian framework. SERRA, Springer Berlin, Vol. 20/3 (2006), 184-205
S. Ankirchner, S. Dereich, P. Imkeller
The Shannon information of filtrations and the additional logarithmic utility of insiders.  Ann. Probab. 34 (2006), No. 2, 743-778
P. Imkeller, I. Pavlyukevich
First exit times of SDEs driven by stable Lévy processes.  Stochastic Processes Appl. 116 (2006), No. 4, 611-642
S. Herrmann, P. Imkeller, D. Peithmann
Transition times and stochastic resonance for multidimensional diffusions with time periodic drift: a large deviations approach.
Ann. Appl. Probab. 16 (2006), No. 4, 1851-1892
M. Fischer, P. Imkeller
Noise induced resonance in bistable systems caused by delay feedback. Stochastic Anal. Appl. 24 (2006), No. 1, 135-194
P. Imkeller, I. Pavlyukevich
Levy flights: transitions and meta-stability.  J. Phys. A, Math. Gen. 39 (2006), No. 15, L237-L246
S. Ankirchner, S. Dereich, P. Imkeller
Enlargement of filtrations and continuous Girsanov-type embeddings.  Donati-Martin, Catherine (ed.) et al., 40th seminar on probability. Berlin: Springer. Lecture Notes in Mathematics 1899 (2007), 389-410
S. Fang, P. Imkeller, T. Zhang
Global flows for stochastic differential equations without global Lipschitz conditions.  Ann. Probab. 35 (2007), No. 1, 180-205
S. Ankirchner, P. Imkeller
Financial markets with asymmetric information: information drift, additional utility and entropy.  Akahori, Jiro (ed.) et al., Stochastic processes and applications to mathematical finance. Proceedings of the 6th Ritsumeikan international symposium, Kyoto, Japan, March 6--10, 2006. Hackensack, NJ: World Scientific. 1-22 (2007)
S. Ankirchner, P. Imkeller, G. Reis
Classical and Variational Differentiability of BSDEs with Quadratic Growth.  Electron. J. Probab. 12 (2007), 1418-1453, electronic only
P. Imkeller, S. Roelly
Die Wiederentdeckung eines Mathematikers: Wolfgang Döblin. (German) [The rediscovery of a mathematician: Wolfgang Doeblin] Mitt. Dtsch. Math.-Ver. 15 (2007) no. 3, 154-159
S. Ankirchner, P. Imkeller, A. Popier
Optimal cross hedging of insurance derivatives.  Stochastic Anal. Appl. 26 (2008), No. 4, 679-709
P. Imkeller, I. Pavlyukevich
Meta-stable behavior of small noise Levy-driven diffusions.  ESAIM Probab. Stat. 12 (2008), 412--437
H. Crauel, P. Imkeller,
Preface Special issue for Prof. Ludwig Arnold's 70th birthday. Part 1,  Stoch. Dyn. Vol. 8 (2008), No 1 v--vi
H. Crauel, P. Imkeller, P. Kloeden, B. Schmalfuß
Preface Special issue for Prof. Ludwig Arnold's 70th birthday. Part 2,  Stoch. Dyn. Vol. 8 (2008), No 3 v--vi
S. Ankirchner, G. Heyne, P. Imkeller
A BSDE approach to the Skorokhod embedding problem for the Brownian motion with drift. Stoch. Dyn. 8 (2008), No. 1, 35-46
P. Imkeller, C. Hein and I. Pavlyukevich
Simple SDE dynamical models interpreting climate data and their meta-stability. Oberwolfach Reports, (2008)
S. Herrmann, P. Imkeller, D. Peithmann
Large deviations and a Kramers' type law for self-stabilizing diffusions. Ann. Appl. Probab. 18 (2008), No. 4, 1379-1423
S. Ankirchner, P. Imkeller, A. Popier
On measure solutions of backward stochastic differential equations. Stoch. Proc. Appl., Vol. 119 (2009), Issue 9, 2744-2772
P. Imkeller, I. Pavlyukevich, T. Wetzel
First exit times for Levy-driven diffusions with exponentially light jumps. Ann. Probab. 37 (2009), No. 2, 530-564
P. Imkeller, G. Reis
Path regularity and explicit truncations order for BSDE with drivers of quadratic growth. Stoch. Proc. Appl. (2010), Vol. 120, No. 3, 348-379
C. Hein, P. Imkeller, I. Pavlyukevich
Limit theorems for p-variations of solutions of SDEs driven by additive Stable Levy noise and model selection for paleo-climatic data. Interdisciplinary Math. Sciences, Vol. 8 (2009), 137-150
P. Imkeller, G. Dos Reis and J. Zhang
Results on numerics for FBSDE with drivers of quadratic growth. Contemporary Quantitative Finance. Essays in Honour of Eckhard Platen (Chiarella, C.; Novikov, A. (Eds.)), Springer Verlag (2010), 159-182
S. Ankirchner, P. Imkeller, G. Reis
Pricing and hedging of derivatives based on non-tradable underlyings. Math. Finance (2010), Vol. 20, No. 2, 289 -312
L. Delong, P. Imkeller
Backward stochastic differential equations with time delayed generators - results and counterexamples. Ann. of Appl. Probab. (2010), Vol. 20, No. 4, 1512-1536
Z. Brzezniak, B.Goldys, P. Imkeller, S. Peszat, E. Priola and J. Zabczyk
Time Irregularity of Generalized Ornstein-Uhlenbeck Processes. C.R.Acad.Sci. Paris Ser. Math. (2010), Vol. 348, 273-276
L. Delong and P. Imkeller
On Malliavin's differentiability of BSDE with time delayed generators driven by Brownian motions and Poisson random measures. Stoch. Proc. Appl. (2010), Vol. 120, No. 9, 1748-1775
S. Ankirchner, P. Imkeller
Hedging with residual risk: a BSDE approach. Seminar on Stochastic Analysis, Random Fields and Applications VI, 311–325, Progr. Probab., 63, Birkhäuser/Springer Basel AG, Basel, 2011.
P. Imkeller, I. Pavlyukevich and M. Stauch
First exit times of non-linear dynamical systems in R^d in perturbed by multifractal Lévy noise. J. Stat. Physics, Vol. 141 (2010), 94-149
A. Debussche, M. Högele and P. Imkeller
Asymptotic first exit times of the Chafee-Infante equation with small heavy-tailed Levy noise. Electronic Communications in Probability 16 (2011), 213-225
P. Imkeller, A.Reveillac and J. Zhang
Solvability and numerical simulation of BSDEs related to BSPDEs with applications to utility maximization. Int. Journal of Theoretical and Applied Finance 14 (2011), 635-667
P. Imkeller, I.Pavlyukevich and T. Wetzel
The hierarchy of exit times of Levy-driven Langevin equations. Eur.Phys.J. Special Topics, Vol. 191 (2010), 211-222
P. Imkeller, A. Reveillac, A. Richter
Differentiability of quadratic BSDE generated by continous martingales and hedging in incomplete markets. Ann. Appl. Probab. 22 (2012), 285-336
J. Gairing, P. Imkeller, C. Hein and I. Pavlyukevich
Dynamical models of climate time series and the rate of convergence of power variations. Mathematisches Forschungsinstitut Oberwolfach, Report No. 40/2011, DOI: 10.4171/OWR/2011/40, (2011)
P. Imkeller, N. S. Namachchivaya, N. Perkowski, C. Yeong
Dimensional reduction in nonlinear filtering: a homogenization approach. Ann. Appl. Probab. 23 (2013), no. 6, 2290–2326.
F. Flandoli, P. Imkeller, C.A. Tudor
2D- stochastic currents over the Wiener sheet. J. Theoret. Probab. 27 (2014), no. 2, 552–575
V. Heinrich, J. Stange, T. Dickhaus, P. Imkeller, U. Krüger, S. Bauer, S. Mundlos, P. N. Robinson, J. Hecht and P. M. Krawitz
The distribution of allele frequencies at heterozygous genomic loci in next generation sequencing data sets. Nucleic Acids Research, Vol. 40, No. 6 (2012), 2426 - 2431
A. Andresen, P. Imkeller, N. Perkowski
Large deviations for Hilbert space valued Wiener processes: a sequence space approach. Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart, Springer Proceedings in Mathematics & Statistics, Vol. 34 (2013), 115 -138
A. Fromm, P. Imkeller and J. Zhang
Existence and stability of measure solutions for BSDE with generators with quadratic growth.  Interdisciplinary Math. Sciences - Vol. 13 (2012), 137-168
U. Horst, Y. Hu, P. Imkeller, A. Reveillac, J. Zhang
Forward-backward systems for expected utility maximization. Stochastic Process. Appl. 124 (2014), no. 5, 1813–1848
J. Gairing, P. Imkeller
Stable CLTs and Rates for Power Variation of α-Stable Lévy Processes. Meth. Comp. Appl. Prob. - Vol. 17(1) (2015), 73-90
P. Imkeller, D. J. Prömel
Existence of Lévy's area and pathwise integration. Communications on Stochastic Analysis - Vol. 9, No. 1 (2015), 93-111
A. Fromm, P. Imkeller, D. Prömel
An FBSDE approach to the Skorokhod embedding problem for Gaussian processes with non-linear drift. Electron. J. Probab. - Vol. 20 (2015), no. 127, 1-38
M. Gubinelli, P. Imkeller and N. Perkowski
Paracontrolled distributions and singular PDEs. Forum Math.Pi - Vol. 3, e6, 75 (2015)
P. Imkeller, N. Perkowski
The existence of dominating local martingale measures. Finance and Stochastics - Vol. 19, No. 4 (2015), 685-717
J. Berner, et al.
Stochastic Parameterization: Towards a new view of Weather and Climate Models. BAMS (2015), 565-588
P. Imkeller, V. Nzengang
Comparison Principle Approach to Utility Maximization. Banach center publications. Vol.105: Stochastic analysis: special volume in honour of Jerzy Zabczyk: Warszawa: Inst. mat. PAN, 2015. - 246 p.: ill. - Incl. bibl. ref. - (2015), 143-158
M. Gubinelli, P. Imkeller, N. Perkowski
A Fourier approach to pathwise stochastic integration. Electron. J. Probab. - Vol. 21 (2016), no. 2, 1-37
P. Imkeller, N. Willrich
Solutions of martingale problems for Lévy-type operators and stochastic differential equations driven by Lévy processes with discontinuous coefficients. Stochastic Process. Appl. 126 (2016), no. 3, 703–734
P. Imkeller, T. Mastrolia, D. Possamai and A. Reveillac
A note on the Malliavin-Sobolev spaces. Statist. Probab. Lett. 109 (2016), 45–53
M. Grigorova, P. Imkeller, E. Offen, Y. Ouknine, M.-C. Quenez
Reflected BSDEs when the obstacle is not right-continuous and optimal stopping.  Annals of Applied Probability 2017, Vol. 27, No. 5, 3153-3188
N. Esmaeli, P. Imkeller
American Options with Asymmetric Information and Reflected BSDE. Bernoulli 24(2) (2018), 1394-1426
N. Esmaeli, P. Imkeller and V. Nzengang
Dynkin Game with Asymmetric Information, Bulletin of the Iranian Mathematical Society, Vol. 45, no. 1, 283-301 (2019)
P. Imkeller, G. dos Reis, W. Salkeld, G. Smith
Differentiability of SDEs with drifts of super-linear growth. Electronic Journal of Probability, Vol. 24, no. 3, 1-43 (2019)

Books

 

P. Imkeller, Jin-Song von Storch
Stochastic Climate Models. Progress in Probability Vol. 49, Birkhäuser Verlag (2001)
P. Imkeller
Malliavin's calculus and applications in stochastic control and finance. IMPAN Lecture Notes 1. Warsaw: Polish Academy of Science, Institute of Mathematics, 83p. (2008)
J. Blath, P. Imkeller, S. Roelly (eds.)
Surveys in Stochastic Processes. EMS Series of Congress Reports. EMS Publishing House (2011)
A. Debussche, M. Högele, P. Imkeller
The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise, Lecture Notes in Mathematics, Vol. 2085, Springer Verlag (2013)
S. Herrmann, P. Imkeller, I. Pavlyukevich, D. Peithmann
Stochastic Resonance - A Mathematical Approach in the Small Noise Limit, Mathematical Surveys and Monographs, Vol. 194, American Mathematical Society (2014)

 


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