**Contact Information**

- matsch$\color{red}{@}$math.sinica.edu.tw
- +886 2 2368-5999 ext. 610
- +886 2 2368-9771

**Research Interests**

- Probability

**Education**

- Ph.D. The University of Minnisota (1980)
- M.S. University of Wisconsin-Milwaukee (1975)
- B.S. National Taiwan University (1972)

**Links**

**Work Experience**

- visiting member University of North Carolina 1989 - 1991
- Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1986 - Present
- Visiting associate professor University of Minnisota 1985 -1986
- Associate Research Fellow Institute of Mathematics, Academia Sinica, R.O.C. 1981 - 1986
- Assistant Professor University of Wisconsin-Milwaukee 1980 - 1981

**Research Descriptions**

The major interest of Dr. Chiang's are Probability theory, Stochastic processes and especially, their applications to Statistics and Mathematical Analysis.

For the system of $d-$dimesnional stochastic differential equations, $d\ge 2$,

$$ \begin{array}{ll} & dX_t^{\epsilon} =b(X_t^{\epsilon})dt+\epsilon dW_t,\ \ \ \ t\in [0,T]\\ & X_0^\epsilon = x \in H\subseteq R^d, \end{array} $$

where $b(x)=(b_1(x),...,b_d(x))$ is a bounded smooth vector field except along the hyperplane $H=\{ x\in R^d, x_1=0\}$ but satisfies the stability condition in the sense that there exists a constants $c>0$ such that for some $\delta_0>0$ $b_1(x)\le -c$ if $x_1\in (0,\delta_0)$ and $b_1(x)\ge c$ if $x_1\in (-\delta_0,0)$, we shall prove that the central limit theorem holds for $(X^\epsilon (\cdot), u^{\epsilon+}(\cdot))$ where $u^{\epsilon+}_t$ is the occupation time of $X^\epsilon(t)$ in the right half space $H^+=\{ x\in R^d, x_1>0\}$ up to time $t$. To be explicit, we shall show that there exist two continuous functions $\phi (\cdot) \in C([0,T],R^d)$ and $\psi(\cdot)\in C([0,T],R)$ such that the process $(\frac{1}{\epsilon}(X^\epsilon(\cdot)-\phi(\cdot)), \frac{1}{\epsilon}(u^{\epsilon+}{(\cdot)}-\psi(\cdot)))$ converges to a Gaussian proess in $C([0,T],R^{d+1})$ in probability thus in distribution as $\epsilon\to 0$.

**Selected Publications**

- "(with S. J., Sheu) The Central Limit Theorem for Diffusion Processes with a Small Parameter in Discontinuous Media"
,
*Frontiers of Chinese Mathematics*, 2015-06. - (with Sheu, Shuenn-Jyi) "A Convexity Approach to Option Pricing with Transaction Costs in Discrete Models"
,
*Stochastic Analysis with Finacial Application*, 65, 300-319, 2011-06. - (with Chow,Yunshyong) "Optimal Ventcel Graphs, Minimal Cost Spanning Trees and Asymptotic Probabilities,"
,
*Applicable Analysis and Discrete Mathematics*, 1, 1-10, 2007-04. - (with Shiu,Shang-Yuan, Sheu, Shuenn-Jhi) "(with S.J.Sheu and S.Y.Shieu) Price systems for markets with transaction costs and control problems for some finance problems"
,
*IMS Lecture Notes-Monograph series Time series and Related Topics*, 52, 257-271, 2006-07. - (with S. J., Sheu) "Small perturbation of diffusions in inhomogeneous media"
,
*Annales de L'I.H.P., Prbas and Stats.*, 38 (3), 285-318, 2002. - (with S. J., Sheu) "Large deviation of diffusion processes with discontinuous drift, Stochastic Analysis and Related Topics VII, The Silivri Workshop. Birkh$\ddot{a}$user" , 159-175, 2001.
- (with Y. Chow and J. Hsieh) "Comparison of Metropolis algorithm and Swendsen-Wang dynamics"
,
*Proceedings of 3rd Sino-Philippine Symposium in Analysis Matimras Matematika, special issue*, 21-31, 2000. - (with Y. Chow) "On the exponential convergence of some inhomogeneous Markov chains"
,
*Soochow J. of Mathematics*, 26 (2), 97-101, 2000. - (with Shuenn-Jyi Sheu) "Large deviation of diffusion processes with discontinuous drift and their occupation times"
,
*Ann. of Probab.*, 28, 140-165, 2000. - (with Yunshyong Chow) "Asymptotic behavior of some linear differential systems"
,
*Journal of Diff. Equ.*, 144 (2), 321-352, 1998. - (with Yunshyong Chow) "On the exit problem from a cycle of simulated annealing processes -- a backword equation approach"
,
*Annals of Appl. Prob.*, 8 (3), 896-916, 1998. - (with Shuenn-Jyi Sheu) "Large deviation of small perturbation of some unstalbe systems"
,
*Journal of Stochastcic Analysis and Applications*, 15 (1), 31-50, 1997. - (with Yunshyong Chow) "Simulated annealing and optimal cooling rates for some 1-dim spin glass models"
,
*Proceedings of Symposia in Pure Mathematics AMS*, 83-93, 1995. - (with Yunshyong Chow) "On global and sharp Markov properties of random functional series in Sobolev spaces"
,
*Theory of Probability and its applications (Russian edition)*, 40 (2), 464-471, 1995. - (with Yunshyong Chow and Y. J. Lee) "Exact formulas of certain functional integrals on Wiener space"
,
*Stochastics and Stochastic Reports*, 50, 211-223, 1994. - (with Yunshyong Chow) "The asymptotic behavior of simulated annealing processes with absorption"
,
*SIAM J. Control and Optimization*, 32 (5), 1247-1265, 1994. - "Mckean-Vlasov equations with discontinuous coefficients"
,
*Soochow Journal of Mathematics*, 20 (4), 507-526, 1994. - (with Yunshyong Chow) "Asymptotic behavior of eigenvalues and radom updating schemes"
,
*Applied Math. and Optimization*, 28, 259-275, 1993. - (with Yunshyong Chow, June Hsieh) "Some limit theorems on simulated annealing"
,
*Lecture Notes in Statistics, Springer-Verlag*, 125-131, 1992. - (with Yunshyong Chow) "A comparison of simulated annealing of Gibbs sampler and Metropolis algorithms"
,
*Lecture Notes in Statistics, Springer-Verlag*, 74, 117-124, 1992. - (with G. Kallianpur, P. Sundar) "Propagation of chaos for systems of interacting neurons"
,
*Pitman Research Notes in Mathematics Seriees*, 268, 98-110, 1992. - (with G. Kallianpur and P. Sundar) "Propagation of chaos and the Mckean-Vlasov equation in duals of nuclear spaces"
,
*Applied Math. and Optimization*, 24, 55-83, 1991. - (with Yunshyong Chow) "A limit theorem for a class of inhomogeneous Markov processes"
,
*Ann. Probability*, 17, 1483-1502, 1989. - (with Yunshyong Chow) "On the convergence rate of annealing processes"
,
*SIAM J. Control Optimization*, 26, 1455-1470, 1988. - (with Shuenn-Jyi Sheu) "(With ) Large deviations of infinite dimensional Ornstein- Uhlenbeck process on C[0, 1]"
,
*Stochastics*, 23, 159-178, 1988. - (with Yunshyong Chow) "On eigenvalues and annealing rates"
,
*Mathematics of Oper. Research*, 13, 508-511, 1988. - (with Chii-Ruey Hwang and Shuenn-Jyi Sheu) "Diffusion for global optimization in $R^n$"
,
*SIAM J. Control Optimization*, 25, 737-757, 1987. - (with Yunshyong Chow and Y.J. Lee) "A formula for $E_W\,{\rm exp}(-2^{-1}a^2|x+y|^2_2)$"
,
*Proc. Amer. Math. Soc.*, 100, 721-724, 1987. - (with Yunshyong Chow) "On the convergence rate of a special class of annealing processes"
,
*Soochow J. Math.*, 13, 23-30, 1987. - "On the lower bound of large deviation of random walks"
,
*Ann. Probability*, 1, 90-96, 1985. - (with Chii-Ruey Hwang) "On the non-uniqueness of the limit points of diffusions with a small parameter"
,
*Stochastics*, 10, 149-153, 1983. - "Large deviations of some Markov processes on compact metric space"
,
*Z. Wahrsch. Verw. Gebiete*, 61, 71-81, 1982. - "A lower bound of the asymptotic behavior of some Markov processes"
,
*Ann. Probability*, 10, 955-967, 1982. - "A note on the irreducibility of Lebesque measure with applications to random walks on the unit circle"
,
*Proc. Amer. Math. Soc.*, 85, 603-605, 1982.