Martingale Problem and Quadratic Family

Haoming Wang

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arXiv · 2509.06016

Martingale Problem and Quadratic Family

Haoming Wang

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Abstract

Assuming uniqueness of the martingale problem for Markov processes of generators $q_t$ in a quadratic family like \[q_t(i,j) = a_t(i) q_0(i,j)^2 + b_t(i) q_0(i,j) - \frac{a_t(i)}{N} \sum_k q_0(i,k)^2,\] where $a_t(i),b_t(i)$ are predictable processes, $N$ is the number of states, and $q_0$ represents the generator of a stationary reference Markov process which satisfies $q_0(i,j)>0$ for all $i,j$, we obtain the sufficient and necessary conditions for the Girsanov transformation.

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Haoming Wang. 2025-09-07. Martingale Problem and Quadratic Family. https://arxiv.org/abs/2509.06016

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