Smoothness of directed chain stochastic differential equations
Copyright policy )Smoothness of directed chain stochastic differential equations
We study the smoothness of the solution of the directed chain stochastic differential equations, where each process is affected by its neighborhood process in an infinite directed chain graph, introduced by Detering et al. (2020). Because of the auxiliary process in the chain-like structure, classic methods of Malliavin derivatives are not directly applicable. Namely, we cannot make a connection between the Malliavin derivative and the first order derivative of the state process. It turns out that the partial Malliavin derivatives can be used here to fix this problem.
25 pages
- University of California, Berkely United States
- University of California United States
- California Digital Library United States
- University of California, Los Angeles United States
- University of California United States
Statistics & Probability, Stochastic calculus of variations and the Malliavin calculus, Statistics, Probability (math.PR), Applications of stochastic analysis (to PDEs, etc.), Interacting random processes; statistical mechanics type models; percolation theory, directed chain stochastic differential equations, Stochastic ordinary differential equations (aspects of stochastic analysis), diffusions on graphs, FOS: Mathematics, partial Malliavin calculus, smoothness, 60H07, 60H30, 60K35, Mathematical Physics, Mathematics - Probability
Statistics & Probability, Stochastic calculus of variations and the Malliavin calculus, Statistics, Probability (math.PR), Applications of stochastic analysis (to PDEs, etc.), Interacting random processes; statistical mechanics type models; percolation theory, directed chain stochastic differential equations, Stochastic ordinary differential equations (aspects of stochastic analysis), diffusions on graphs, FOS: Mathematics, partial Malliavin calculus, smoothness, 60H07, 60H30, 60K35, Mathematical Physics, Mathematics - Probability
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