On strong solutions for positive definite jump diffusions
Copyright policy )On strong solutions for positive definite jump diffusions
We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which have recently been extensively employed in financial mathematics. Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the alpha-th positive semidefinite power of the process itself with 0.5
version to appear in Stochastic Processes and Their Applications, 2011
- University of Vienna Austria
- TUM Institute for Advanced Study
- Technical University of Munich Germany
- University of Ulm Germany
- TECHNISCHE UNIVERSITAET MUENCHEN Germany
Statistics and Probability, stochastic differential equations on open sets, Affine diffusions, 60G51, 60H10, 60J60, 60J75, matrix subordinators, Processes with independent increments; Lévy processes, Stochastic differential equations on open sets, Modelling and Simulation, FOS: Mathematics, local martingales on stochastic intervals, Diffusion processes, Strong solutions, jump diffusion processes on positive definite matrices, Applied Mathematics, Probability (math.PR), Wishart processes, affine diffusions, Matrix subordinators, Stochastic ordinary differential equations (aspects of stochastic analysis), Jump diffusion processes on positive definite matrices, strong solutions, Jump processes, Mathematics - Probability, Local martingales on stochastic intervals
Statistics and Probability, stochastic differential equations on open sets, Affine diffusions, 60G51, 60H10, 60J60, 60J75, matrix subordinators, Processes with independent increments; Lévy processes, Stochastic differential equations on open sets, Modelling and Simulation, FOS: Mathematics, local martingales on stochastic intervals, Diffusion processes, Strong solutions, jump diffusion processes on positive definite matrices, Applied Mathematics, Probability (math.PR), Wishart processes, affine diffusions, Matrix subordinators, Stochastic ordinary differential equations (aspects of stochastic analysis), Jump diffusion processes on positive definite matrices, strong solutions, Jump processes, Mathematics - Probability, Local martingales on stochastic intervals
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