Estimates of Certain Exit Probabilities for $p$-Adic Brownian Bridges
| Autor: | David Weisbart |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Diffusion equation General Mathematics Operator (physics) Probability (math.PR) 010102 general mathematics Mathematical analysis 60G22 (Primary) 11S82 60G51 (Secondary) FOS: Physical sciences Mathematical Physics (math-ph) Space (mathematics) 01 natural sciences Measure (mathematics) Prime (order theory) 010104 statistics & probability FOS: Mathematics Fundamental solution Exponent 0101 mathematics Statistics Probability and Uncertainty Brownian motion Mathematics - Probability Mathematical Physics Mathematics |
| Popis: | For each prime $p$, a diffusion constant together with a positive exponent specify a Vladimirov operator and an associated $p$-adic diffusion equation. The fundamental solution of this pseudo-differential equation gives rise to a measure on the Skorokhod space of $p$-adic valued paths that is concentrated on the paths originating at the origin. We calculate the first exit probabilities of paths from balls and estimate these probabilities for the brownian bridges. 19 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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