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• W4387028503 abstract "We develop a new technique for the path approximation of one-dimensional stochastic processes. Our results apply to the Brownian motion and to some families of stochastic differential equations whose distributions could be represented as a function of a time-changed Brownian motion (usually known as $ L $ and $ G $-classes). We are interested in the $ varepsilon $-strong approximation. We propose an explicit and easy-to-implement procedure that jointly constructs, the sequences of exit times and corresponding exit positions of some well-chosen domains. In our main results, we prove the convergence of our scheme and how to control the number of steps, which depends on the covering of a fixed time interval by intervals of random sizes. The underlying idea of our analysis is to combine results on Brownian exit times from time-depending domains (one-dimensional heat balls) and classical renewal theory. Numerical examples and issues are also developed in order to complete the theoretical results." @default.
• W4387028503 created "2023-09-26" @default.
• W4387028503 creator A5042496159 @default.
• W4387028503 creator A5056464748 @default.
• W4387028503 date "2023-01-01" @default.
• W4387028503 modified "2023-10-18" @default.
• W4387028503 title "Strong approximation of some particular one-dimensional diffusions" @default.
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• W4387028503 doi "https://doi.org/10.3934/dcdsb.2023164" @default.
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