[1] Moshe Zakai was born in Sokółka, Poland, to his parents Rachel and Eliezer Zakheim with whom he immigrated to Israel in 1936.

He joined the scientific department of the Defense Minister of Israel, where he was assigned to research and development of radar systems.

From 1956 to 1958, he did graduate work at the University of Illinois on an Israeli Government Fellowship, and was awarded the PhD in electrical engineering.

The results for this case were highly complicated and were initially studied by Stratonovich in 1959 - 1960 and later by Kushner in 1964, leading to the Kushner-Stratonovich equation, a non-linear stochastic partial differential equation (SPDE) for the conditional probability density representing the optimal filter.

Around 1967, Zakai derived a considerably simpler SPDE for an unnormalized version of the optimal filter density.

White noise and Brownian motion (the Wiener process) are functions of a single parameter, namely time.

The papers of Zakai with David Nualart, Ali Süleyman Üstünel and Zeitouni promoted the understanding and applicability of the Malliavin calculus.